From the U.S. patent application Ser. No. 689,231, filed Jun. 12, 1991, now U.S. Pat. No. 5,213,399, the hydraulic switching concept of a dual circuit brake system with brake slip control is already known which provides, between a brake pressure generator and the wheel brakes, a low-pressure and high-pressure accumulator system used to either supply the pressure accumulator system with a pressure fluid volume or to draw pressure fluid from it, in dependence upon the switching position of a valve arrangement. The shown high-pressure system comprises an auxiliary pressure pump, each associated with a brake pressure control circuit, which auxiliary pressure pump draws pressure fluid from the preceding low-pressure accumulator in order to supply it to the wheel brakes during a brake slip control action and/or also to the high-pressure accumulator in dependence upon the quantity of pressure fluid actually required. Due to the considerable circuit complexity needed for a brake pressure control action within two brake circuits, the required ability of functional parts to be integrated, which would lead to a brake system of compact design, cannot be achieved.